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# Expectation and Variance

The expectation of a random variable,

$E(X)$

, is the average of possible values weighted by their probabilities. Formally, it can be defined in two ways:- 1.Domain definition:$E(X) = \sum_{\omega \in \Omega} X(\omega) P(\omega)$.
- 2.Range definition:$E(X) = \sum_x x P(X = x)$.

Expectation has nice properties of linearity:

$E(X + Y) = E(X) + E(Y)$

and $E(aX + b) = aE(x) + b$

.